Equilibrium Question 901
Question: A solution saturated in lime water has a pH of 12.4. Then the Ksp for $ Ca{{(OH)}_2} $ is:
Options:
A) $ 3.2\times {10^{-3}} $
B) $ 7.8\times {10^{-6}} $
C) $ 7.8\times {10^{-28}} $
D) $ 3.2\times {10^{-4}} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ pH=12.4 $
$ \Rightarrow $ $-\log ({H^{+}})=12.4,\Rightarrow $
$ \log [{H^{+}}]=13.6 $
$ Ca{{(\overset{+}{\mathop{OH}},)}_2}\rightarrow 2OH+C{a^{2+}} $
$ [{H^{+}}]=4\times {10^{-13}} $
$ [O{H^{-}}]=\frac{{10^{-14}}}{4\times 10}=\frac{1}{3}\times {10^{-1}}=2.5\times {10^{-2}} $
$ Ksp=[C{a^{2+}}][O{H^{-}}] $
$ [C{a^{2+}}]=\frac{1}{2}[O{H^{-}}] $
$ ( \frac{1}{8}\times {10^{-1}} ){{( \frac{1}{4}\times {10^{-1}} )}^{2}}=\frac{1}{8}\times \frac{1}{16}\times {10^{-3}} $
$ 7.8\times {10^{-6}} $
